Commutative S-algebras of prime characteristics and applications to unoriented bordism

TL;DR

This paper develops the theory of highly structured ring spectra of prime characteristic, exemplified by S//p, and explores their relationships with Thom spectra like MO, including computations of Hochschild and Andre9-Quillen invariants.

Contribution

It introduces a precise notion of prime characteristic ring spectra, studies their properties via S//p, and relates them to Thom spectra such as MO, with explicit invariant computations.

Findings

S//p can be realized as Thom spectra.

S//p is not a commutative algebra over HF_p.

MO is not a polynomial algebra over S//2.

Abstract

The notion of highly structured ring spectra of prime characteristic is made precise and is studied via the versal examples S//p for prime numbers p. These can be realized as Thom spectra, and therefore relate to other Thom spectra such as the unoriented bordism spectrum MO. We compute the Hochschild and Andr\'e-Quillen invariants of the S//p. Among other applications, we show that S//p is not a commutative algebra over the Eilenberg-Mac Lane spectrum HF_p, although the converse is clearly true, and that MO is not a polynomial algebra over S//2.